Problem

Use transformations of the absolute value function, f(x)=|x|, to graph the function g(x)=-4|x+6|-5. What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)?

Solution

Step 1 :The function g(x)=-4|x+6|-5 is a transformation of the absolute value function f(x)=|x|.

Step 2 :The transformations needed are a horizontal shift of 6 units to the left, indicated by the '+6' inside the absolute value function.

Step 3 :The function is also shifted 5 units down, indicated by the '-5' outside the absolute value function.

Step 4 :The function is stretched by a factor of 4, indicated by the '-4' outside the absolute value function.

Step 5 :Finally, the function is reflected over the x-axis, indicated by the negative sign outside the absolute value function.

Step 6 :\(\boxed{\text{The transformations needed to obtain the graph of } g(x) \text{ from the graph of } f(x) \text{ are a horizontal shift of 6 units to the left, a vertical shift of 5 units down, a vertical stretch by a factor of 4, and a reflection over the x-axis.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20096/

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